• PDF / 2,323,696 Bytes
• 7 Pages / 612 x 792 pts (letter) Page_size
• 82 Downloads / 304 Views

DOWNLOAD

REPORT

---

I.

INTRODUCTION

THE grain-coarsening behavior of steels during reheating for hot rolling is an important factor in the design of thermomechanical processing to achieve fine-grained product. In the course of studies of thermomechanical treatment of microalloyed steels, a body of grain-coarsening data has been accumulated for C-Mn-Si base steels and for steels of this base composition with additions of A1, V, Ti, or Nb. These observations are summarized, and the patterns that evolve are interpreted in terms of models of pinning of grain boundaries by precipitate particles. Most models of particle pinning of grain boundaries 1-~are modifications of the Zener concept and therefore reduce to a similar formulation. Zener's model 1 balances the force (27/R) that arises from the decrease in grain-boundary area per volume (thus energy) during the growth of an isolated grain of radius R (assumed equal to the radius of curvature) and grain-boundary energy 7, against the pinning force (TrrnsT) caused by a density ns of particles of radius r in the boundary. For pinning, nsr = E l / R , where sc = 2/7r for the Zener formulation, but varies with the details of the model. If there is no segregation to boundaries or sweeping up of particles by boundaries, the boundary simply samples the volume average, nv, of particles that lie within + r of the plane of the boundary. Thus, the pinning condition is nvRr 2 = ~'

this case ~:" = 7r/6 [(3/2 - 2/Z)] where Z is the ratio of diameters of the growing and pinned grains. For the normally observed range o f Z = ~/2 to 2, ~" = 0.05 to 0.26. Hellman and Hillert3 considered the effects of the ratio of boundary curvature radius to particle radius, the relation between curvature and grain-size distribution, and particlesize distribution to arrive at approximate relations for normal and abnormal grain growth. For small volume fractions of particles, ~:" = 4/9 for normal growth, and ~:" < 4 / 3 for abnormal growth. Figure 1 shows the size D of the grains pinned by a given value of d/iv according to these three models. 1'2'3 The predicted size varies by over an order of magnitude, depending upon the assumptions of the model. In all the models, however, the same trend exists. To maintain a fine grain size requires a large volume fraction of very fine precipitates. These two parameters, fv and d, are fixed initially by the level of microalloy additions and the prior thermomechanical treatment of the steel. However, changes that occur during subsequent reheating for hot rolling, for example, depend entirely on the rate of dissolution of particles, which is fixed by the type of microalloy addition. Particle dissolution has two effects: a direct effect in reducingfv and an indirect effect of increasing the rate of particle ripening (increasing d) by providing the higher solute level

[1] 103

f

where ~' = 1/ 7r in the Zener model. In terms of the volume fraction of spherical particles, iv = 4/3 7rr3nv, the relation becomes d D = sc'--

iv

[la]

where the diameters d = 2r for particles and D = 2R for